Eye of Horus, Session 1: More Things in Heaven and Earth
September 17, 2013
As kids trickled into our first day of Math Circle for eight-to-ten year olds, the group played Tens Concentration. Silence engulfed the room during enthusiastic play until M asked whether she could ask for help from the group. “It’s up to all of you,” I responded to the group. “It’s your game.” Noise erupted. Help and dubious help were offered. Y suggested an alternative version of the game, which I promised to try another day. Play continued until all the cards were picked up. I collected the cards without asking for counts, and started asking questions.
“Why are we not counting who got how many matches?”
“Because Math Circle is cooperative,” answered M, a veteran.
“What was the point of that game?” I asked.
“To get better at adding up to ten?” responded S tentatively.
“I think you’re already pretty good at that. There must be some other reason.” The silence returned. “Why do you think the word concentration is in the name of the game?”
“It helps with concentration and attention!” said several kids.
“Why are we here?” I asked.
“To learn math.”
“What is math?”
“Numbers,” said S.
“It’s more than that,” I prompted.
“Adding,” added someone.
“Yes, but math covers more than just numbers. What else?”
M remembered similar discussions in prior Math Circles when she asked, “There’s math in everything, right?” I set that question aside for now, and asked for more specifics. I wish I had thought to quote Shakespeare here. (“There are more things in heaven and earth than are dreamt of in your philosophy.”) People were thinking hard.
Finally, R chimed in “Shapes!” The kids were curious and excited. I promised to extend this discussion for weeks. Then I returned to my questions.
“What is a number?” Many ideas emerged. So far, our working definition is that it’s a device for counting. I attempted to move from the concrete to the abstract by discussing the difference between numerals, numbers, and things. This was quite confusing. I made the analogy between this system and the letter-word-thing system in writing, but not everyone understood. Movement toward abstract thinking is a goal in math, but not something that is natural to young children.
We moved back to the concrete with some ancient mythology. I read aloud the part of Ovid’s Metamorphosis that introduces Narcissus. We discussed it, and I showed some art from across the ages that depicts Narcissus. E, D, R, and M were familiar with him from Rick Riordan’s Percy Jackson novels. We discussed what it means to be narcissistic. Then I asked, “How could a number be narcissistic?”
Many possibilities arose:
- a number in which the digits copy themselves (i.e. 11, 22, 55)
- a number added to itself
- an even number because it can split itself into two whole numbers, which can then rejoin to reform the original number
- multiples of numbers that have repeating digits
“Which is right?” demanded the kids. I explained that all of them could be right. That in fact, you could invent your own kind of number and give it your name or a name you like. Someone even invented vampire numbers. “Who thought of these things?” asked the kids. I don’t know, but would like to. (If you are reading this and do know, would you kindly email me?)
We had some wooden cubes on the floor that the kids were playing with, so I asked them to show me their own versions of “narcissistic numbers.” As they worked, I explained that the numbers that are commonly called narcissistic are even more in love with themselves that what we thought of so far. The blocks triggered more possibilities:
- numbers that you can turn upside down and have the same number
- numbers that you can turn upside down and are still some number
- numbers that mark important ages/transitions in people’s lives (10, 16, 18, 21, 40, 50)
- numbers that are symmetrical
We ended our session with the kids starting to ask the questions instead of me. In just one hour, we had engaged in a number of important parts of mathematical thinking and discovery: asking questions, precisely defining terms, and working collaboratively. I wasn’t sure whether a group of 13 would work well collaboratively. For the most part, it did. A few kids said very little, so I will work on that next time. I also want to work on getting across the idea that math is more than arithmetic.
Thanks for coming and for reading.
Sounds like a great start to a new year. I’m so excited to have my children learning to think about math rather than just learning to “do” math. Thanks, Rodi!